First slide

Doppler

Question

A source of sound approaches an observer and the apparent frequency of sound heard by the observer is f. When the source remains stationary and the observer approaches the source with same velocity apparent frequency heard by the observer is $\frac{15 f}{16}$ . If velocity of sound in air is 330 m/s, velocity of source is

Moderate

A

68 m/s
B

82.5 m/s
C

17 m/s
D

55.5 m/s

Solution

(2)
$\begin{array}{l} w h e n s o u r c e i s m o v i n g, f = \frac{f_{0}}{(1 - \frac{V}{V_{S}})} \\ w h e n o b s e r v e r i s m o v i n g, \frac{15 f}{16} = f_{0} (1 + \frac{V}{V_{S}}) \\ ∴ \frac{15 f}{16 (1 - \frac{V}{V_{S}})} = (1 + \frac{V}{V_{S}}) \\ \Rightarrow {(\frac{V}{V_{S}})}^{2} = 1 - \frac{15}{16} = \frac{1}{16} \\ \Rightarrow V = \frac{V_{S}}{4} = \frac{330}{4} m / s = 82.5 m / s \end{array}$

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